On the other hand, let us look at this issue from a physical
viewpoint. The lowest order memory function defines (via the
Green-Kubo relations [1]}) the generalized
self-diffusion coefficient \(\tilde{D}(\omega )\) . In its turn, the
highest order SCF \(\Gamma _s\)  generates the cut-off frequency, at
which the real part of \(\tilde{D}(\omega )\)  vanishes, whereas the
imaginary part of the above mentioned coefficient remains
different from zero. The real part of \(\tilde{D}(\omega )\)  is known
to be associated with the energy dissipation by diffusion. Since
\(\Re \big [\tilde{D}(\omega \geqslant \omega _{\textrm {c}})\big ]=0\) , there appears a
“narrowing” of the dissipation channel from high
frequencies. At the same time, the imaginary part
\(\Im \big [\tilde{D}(\omega \geqslant \omega _{\textrm {c}})\big ]> 0\)  contributes to the
vibrational mode of the fluid due to a renormalization of the
corresponding excitation. This underdamped high frequency
excitation can cause a non-monotonous behaviour of the VAFs at long
times.
